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Simplifying n2 + 4n = 91 Reorder the terms: 4n + n2 = 91 Solving 4n + n2 = 91 Solving for variable 'n'. Reorder the terms: -91 + 4n + n2 = 91 + -91 Combine like terms: 91 + -91 = 0 -91 + 4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '91' to each side of the equation. -91 + 4n + 91 + n2 = 0 + 91 Reorder the terms: -91 + 91 + 4n + n2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + 4n + n2 = 0 + 91 4n + n2 = 0 + 91 Combine like terms: 0 + 91 = 91 4n + n2 = 91 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = 91 + 4 Reorder the terms: 4 + 4n + n2 = 91 + 4 Combine like terms: 91 + 4 = 95 4 + 4n + n2 = 95 Factor a perfect square on the left side: (n + 2)(n + 2) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (n + 2) equal to 9.746794345 and -9.746794345.Subproblem 1
n + 2 = 9.746794345 Simplifying n + 2 = 9.746794345 Reorder the terms: 2 + n = 9.746794345 Solving 2 + n = 9.746794345 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 9.746794345 + -2 Combine like terms: 2 + -2 = 0 0 + n = 9.746794345 + -2 n = 9.746794345 + -2 Combine like terms: 9.746794345 + -2 = 7.746794345 n = 7.746794345 Simplifying n = 7.746794345Subproblem 2
n + 2 = -9.746794345 Simplifying n + 2 = -9.746794345 Reorder the terms: 2 + n = -9.746794345 Solving 2 + n = -9.746794345 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -9.746794345 + -2 Combine like terms: 2 + -2 = 0 0 + n = -9.746794345 + -2 n = -9.746794345 + -2 Combine like terms: -9.746794345 + -2 = -11.746794345 n = -11.746794345 Simplifying n = -11.746794345Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.746794345, -11.746794345}
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